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In 2+1 dimensions the global U($2N$) symmetry associated with massless Diracfermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I willshow how to adapt the domain wall formulation to recover the U($2N$)-invariantlimit in interacting fermion models as the domain wall separation is increased.In particular, I will focus on the issue of potential dynamical mass generationin the Thirring model, postulated to take place for $N$ less than some critical$N_c$. I will present results of simulations of the model using both HMC($N=2$) and RHMC ($N=1$) algorithms, and show that the outcome is verydifferent from previous numerical studies of the model made with staggeredfermions, where the corresponding pattern of symmetry breaking is distinct.

Numerical study of the $2+1d$ Thirring model with U($2N$)-invariant fermions